# Finding Laurent Series

This was an exam question and I was absolutely lost.

Find positive constants $a,b$ such that the function

$$\frac{1}{z^2+a} + \frac{1}{z+b}$$

has three Laurent series, one for each of the domains $|z|<1, \,\, 1<|z|<4, \,\, |z|>4$.

## migrated from math.meta.stackexchange.comApr 19 '13 at 19:57

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Try $a=1$ and $b=4$ or $a=16$ and $b=1$.